Digital scopes are working their hardest when they are armed and waiting for a trigger but haven't triggered yet. Each active channel's buffers are circulating digitized data (similar to a crash recorder in an airplane) just waiting for the trigger to validate and the process stops. If the trigger was in the middle of a 10 M memory, the scope would continue to take 5 M samples and stop. The first 5 M samples would be pre-trigger and the second 5 M samples would be post trigger. Seeing what signals are doing that leads up to the trigger event is a very powerful troubleshooting tool.
Consider that in the above example, no data is missed waiting for the valid trigger condition. The scope is constantly looking waiting for a keyed RF waveform to be at a high enough level to trigger. This is a powerful condition that points to a potential concern. If we can't trigger on the waveforms we need to see, we have a real problem. This should be central issue in selecting which scope to use.
Most oscilloscopes will let you trigger on the width of pulses (glitch), the intervals between pulses, the logical or pattern conditions between inputs, after specific delays by events or time, drop out conditions, etc. Trigger Icons symbolically relate how the current trigger selection is working. This is very helpful if you are looking at a screen shot later and trying to reacquire with the same trigger conditions.
How fast can a digital scope re-arm and trigger?
The maximum trigger rate is a key specification that determines how often you can view what is of interest. There are so many variables of memory length and processing loads that usually example benchmark measurements are taken to establish trigger times. Some scopes have a memory segmentation feature that lets you trigger very rapidly and fill just a portion (1 segment out of n segments per trigger). This is commonly referred to as Sequence Mode and speeds of 1 M triggers per second are common.
What is a software trigger?
Some scopes let you define a software trigger based on a measurement. This can be very good at finding portions of your signal that are outside of a specification margins.
Oscilloscopes can almost always capture single shot events but not always with the amount of pre or post trigger delay you might need. If your application requires capturing a lot of transient waveforms, look into the span of trigger delay.
Not all scopes have a Trigger BW that match the input channel's BW specifications. Be certain you can trigger on the highest frequency you need.